Question: Solve for $x$ and $y$ using elimination. ${5x-y = 23}$ ${-4x+y = -18}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-y = 23}\thinspace$ to find $y$ ${5}{(5)}{ - y = 23}$ $25-y = 23$ $25{-25} - y = 23{-25}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 5}$ into $\thinspace {-4x+y = -18}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ + y = -18}$ ${y = 2}$